Andre Andrey Kolmogorov gave an axiomatic definition of probability in 1933, as follows:

Let E be a random experiment and S be its sample space. For each event A of E, assign a real number, which is recorded as P(A), which is called the probability of event A. Here, P(A) is a set function, and P(A) must meet the following conditions:

(1) Nonnegativity: For each event A, there is P(A)≥0.

(2) Normality: for inevitable events, there is p (ω) = 1.

(3) Countable additivity: Let A 1, A2…… ...... become mutually incompatible events, that is, for i≠j, Ai∩Aj=φ, (I, J = 1, 2 ...), and then P (A/kloc.

Axiomatic probability theory;

Kolmogorov's axiomatic system of probability theory is mainly rooted in set theory, measure theory and real variable function theory.

Using the skillful theory of real variable function, he established the analogy between set measure and probability of random events, integration and mathematical expectation, orthogonality of functions and independence of random variables. This extensive analogy endows probability theory with the characteristics of deductive mathematics, and many integral theorems on a straight line can be transplanted to probability space.